Pricing Perpetual American Compound Options under a Matrix-Exponential Jump-Diffusion Model

ABSTRACT

This paper considers the problem of pricing perpetual American compound options under a matrix-exponential jump-diffusion model. The rational prices of these options are defined as the value functions of the corresponding optimal stopping problems. The general optimal stopping theory and the averaging method for solving the optimal stopping problems are applied to find the value functions and the optimal stopping times and thereby to determine the rational prices and the optimal boundaries of these perpetual American compound options. Explicit formulae for the rational prices and the optimal boundaries are also obtained for hyper-exponential jump-diffusion models.

KEY WORDS:

• Option pricing
• perpetual American compound option
• optimal stopping problem
• jump-diffusion process

Acknowledgments

The authors would like to thank National Center for Theoretical Sciences (NCTS), Institute of Mathematical Modeling and Scientific Computation (MMSC) and the National Science Council, Taiwan, for financially supporting this research under the contract number: Most 103-2115-M-009-009. Ted Knoy is appreciated for his editorial assistance.